Question: In this square array of 16 dots, four dots are to be chosen at random. What is the probability that the four dots will be collinear? Express your answer as a common fraction.

[asy]
size(59);
for(int i = 0; i<4; ++i)
for(int j = 0; j<4; ++j)
dot((i,j),linewidth(7));
[/asy]
Solution: If all four of the dots are collinear, it is obvious that it must either be a horizontal line of dots, a vertical line of dots, or a diagonal line of dots. And inspection tells us that there are $4 + 4 + 2 = 10$ such collinear sets of 4. And in total, there are ${16 \choose 4} = \frac{16\cdot 15 \cdot 14 \cdot 13}{4 \cdot 3 \cdot 2} = 2 \cdot 5 \cdot 13 \cdot 14 = 1820$. So, the probability is $\frac{10}{1820} = \boxed{\frac{1}{182}}$.